0.00/0.00	% File    : /export/starexec/sandbox2/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : original
0.00/0.00	% Variant    : purification_ext
0.00/0.00	% Ordering    : kbo
0.00/0.00	% Command    : 
0.00/0.00	#!/bin/sh
0.00/0.00	
0.00/0.00	./zipperposition.native ${1:+"$1"} \
0.00/0.00	  -i tptp \
0.00/0.00	  -o tptp \
0.00/0.00	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.00	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.00	  --no-avatar \
0.00/0.00	  --ho \
0.00/0.00	  --force-ho \
0.00/0.00	  --no-ho-elim-pred-var \
0.00/0.00	  --ho-general-ext-pos \
0.00/0.00	  --no-ho-unif \
0.00/0.00	  --no-induction \
0.00/0.00	  --no-unif-pattern \
0.00/0.00	  --ord $2  \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --ho-purify ext \
0.00/0.00	  --ho-ext-axiom \
0.00/0.00	  --restrict-hidden-sup-at-vars \
0.00/0.00	  --ho-prim-enum none \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --dont-select-ho-var-lits \
0.00/0.00	  --no-fool
0.00/0.19	% Computer   : n097.star.cs.uiowa.edu
0.00/0.19	% Model      : x86_64 x86_64
0.00/0.19	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.19	% Memory     : 32218.625MB
0.00/0.19	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.19	% CPULimit   : 300
0.00/0.19	% DateTime   : Fri Feb  2 17:20:09 CST 2018
2.24/2.50	% done 1211 iterations in 2.297s
2.24/2.50	% SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
2.24/2.50	% SZS output start Refutation
2.24/2.50	tff(cTHM531E_pme, conjecture,
2.24/2.50	  (((![Xx:a]: (cB(Xx) => cC(Xx))) & 
2.24/2.50	    (![P:(a > $o > $o)]:
2.24/2.50	       (((![Y:(a > $o),Xx:a,Z:(a > $o)]:
2.24/2.50	            (((![Xx_27:a]: (Z(Xx_27) => ((Xx_27 = Xx) | Y(Xx_27)))) & P(Y)) =>
2.24/2.50	             P(Z))) & 
2.24/2.50	         (![E:(a > $o)]: ((~(?[Xt:a]: E(Xt))) => P(E)))) =>
2.24/2.50	        P(cC)))) =>
2.24/2.50	   (![P:(a > $o > $o)]:
2.24/2.50	      (((![Y:(a > $o),Xx:a,Z:(a > $o)]:
2.24/2.50	           (((![Xx_28:a]: (Z(Xx_28) => ((Xx_28 = Xx) | Y(Xx_28)))) & P(Y)) =>
2.24/2.50	            P(Z))) & 
2.24/2.50	        (![E:(a > $o)]: ((~(?[Xt:a]: E(Xt))) => P(E)))) =>
2.24/2.50	       P(cB))))).
2.24/2.50	tff(zf_stmt_0, negated_conjecture,
2.24/2.50	  (~
2.24/2.50	    (((![Xx:a]: (cB(Xx) => cC(Xx))) & 
2.24/2.50	      (![P:(a > $o > $o)]:
2.24/2.50	         (((![Y:(a > $o),Xx:a,Z:(a > $o)]:
2.24/2.50	              (((![Xx_27:a]: (Z(Xx_27) => ((Xx_27 = Xx) | Y(Xx_27)))) & P(Y)) =>
2.24/2.50	               P(Z))) & 
2.24/2.50	           (![E:(a > $o)]: ((~(?[Xt:a]: E(Xt))) => P(E)))) =>
2.24/2.50	          P(cC)))) =>
2.24/2.50	     (![P:(a > $o > $o)]:
2.24/2.50	        (((![Y:(a > $o),Xx:a,Z:(a > $o)]:
2.24/2.50	             (((![Xx_28:a]: (Z(Xx_28) => ((Xx_28 = Xx) | Y(Xx_28)))) & P(Y)) =>
2.24/2.50	              P(Z))) & 
2.24/2.50	          (![E:(a > $o)]: ((~(?[Xt:a]: E(Xt))) => P(E)))) =>
2.24/2.50	         P(cB)))))).
2.24/2.50	tff('0', plain, ![X4 : a > $o]: (sk_P(X4) | X4(sk_Xt(X4))),
2.24/2.50	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.24/2.50	tff('1', plain,
2.24/2.50	    ![X4 : a > $o, X5 : a > $o]: (X5 != X4 | sk_P(X4) | X5(sk_Xt(X4))),
2.24/2.50	    inference('ho.purify_applied_variable', [status(thm)], ['0'])).
2.24/2.50	tff('2', plain,
2.24/2.50	    ![X1 : a > $o > $o, X2 : a]: (X1(cC) | ~ sk_E(X1, X2) | X1(sk_Y(X1))),
2.24/2.50	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.24/2.50	tff('3', plain,
2.24/2.50	    ![X1 : a > $o > $o, X2 : a, X3 : a > $o > $o, X4 : a > $o > $o]:
2.24/2.50	      (X4 != X1 | X3 != X1 | X1(cC) | ~ sk_E(X3, X2) | X4(sk_Y(X3))),
2.24/2.50	    inference('ho.purify_applied_variable', [status(thm)], ['2'])).
2.24/2.50	tff('4', plain,
2.24/2.50	    ![X0 : a > $o > $o, X1 : a > $o > $o, X2 : a]:
2.24/2.50	      (X0(sk_Y(X1)) | ~ sk_E(X1, X2) | X1(cC) | X0 != X1),
2.24/2.50	    inference('eq_res', [status(thm)], ['3'])).
2.24/2.50	tff('5', plain,
2.24/2.50	    ![X0 : a > $o > $o, X1 : a > $o > $o, X2 : a, X3 : a > $o > $o]:
2.24/2.50	      (X3 != X1 | X0(sk_Y(X1)) | ~ sk_E(X1, X2) | X3(cC) | X0 != X1),
2.24/2.50	    inference('ho.purify_applied_variable', [status(thm)], ['4'])).
2.24/2.50	tff('6', plain,
2.24/2.50	    ![X5 : a > $o, X6 : a > $o, X7 : a]:
2.24/2.50	      (~ sk_P(X5) | X6(sk_Xx_28(X6, X7, X5)) | sk_P(X6)),
2.24/2.50	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.24/2.50	tff('7', plain,
2.24/2.50	    ![X5 : a > $o, X6 : a > $o, X7 : a, X8 : a > $o]:
2.24/2.50	      (X8 != X6 | ~ sk_P(X5) | X6(sk_Xx_28(X8, X7, X5)) | sk_P(X8)),
2.24/2.50	    inference('ho.purify_applied_variable', [status(thm)], ['6'])).
2.24/2.50	tff('8', plain, ![X0 : a]: (cC(X0) | ~ cB(X0)),
2.24/2.50	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.24/2.50	tff('9', plain,
2.24/2.50	    ![X0 : a > $o, X1 : a, X2 : a > $o]:
2.24/2.50	      (~ $true | sk_P(X2) | ~ sk_P(X0) | X2 != cB | cC(sk_Xx_28(X2, X1, X0))),
2.24/2.50	    inference('sup-', [status(thm)], ['7', '8'])).
2.24/2.50	tff('10', plain,
2.24/2.50	    ![X0 : a > $o, X1 : a, X2 : a > $o]:
2.24/2.50	      (cC(sk_Xx_28(X2, X1, X0)) | X2 != cB | ~ sk_P(X0) | sk_P(X2)),
2.24/2.50	    inference('simplify', [status(thm)], ['9'])).
2.24/2.50	tff('11', plain,
2.24/2.50	    ![X5 : a > $o, X6 : a > $o, X7 : a]:
2.24/2.50	      (~ sk_P(X5) | ~ X5(sk_Xx_28(X6, X7, X5)) | sk_P(X6)),
2.24/2.50	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.24/2.50	tff('12', plain,
2.24/2.50	    ![X5 : a > $o, X6 : a > $o, X7 : a, X8 : a > $o]:
2.24/2.50	      (X8 != X5 | ~ sk_P(X5) | ~ X8(sk_Xx_28(X6, X7, X5)) | sk_P(X6)),
2.24/2.50	    inference('ho.purify_applied_variable', [status(thm)], ['11'])).
2.24/2.50	tff('13', plain,
2.24/2.50	    ![X0 : a > $o, X2 : a > $o]:
2.24/2.50	      (~ $true
2.24/2.50	       | sk_P(X2)
2.24/2.50	       | ~ sk_P(X0)
2.24/2.50	       | X2 != cB
2.24/2.50	       | sk_P(X2)
2.24/2.50	       | ~ sk_P(X0)
2.24/2.50	       | cC != X0),
2.24/2.50	    inference('sup-', [status(thm)], ['10', '12'])).
2.24/2.50	tff('14', plain,
2.24/2.50	    ![X0 : a > $o, X2 : a > $o]:
2.24/2.50	      (cC != X0 | X2 != cB | ~ sk_P(X0) | sk_P(X2)),
2.24/2.50	    inference('simplify', [status(thm)], ['13'])).
2.24/2.50	tff('15', plain, ~ sk_P(cB), inference('cnf', [status(esa)], [zf_stmt_0])).
2.24/2.50	tff('16', plain,
2.24/2.50	    ![X0 : a > $o]: (~ $true | ~ sk_P(X0) | cB != cB | cC != X0),
2.24/2.50	    inference('sup-', [status(thm)], ['14', '15'])).
2.24/2.50	tff('17', plain, ![X0 : a > $o]: (cC != X0 | ~ sk_P(X0)),
2.24/2.50	    inference('simplify', [status(thm)], ['16'])).
2.24/2.50	tff('18', plain,
2.24/2.50	    ![X0 : a > $o > $o, X1 : a > $o > $o, X2 : a]:
2.24/2.50	      (~ $true
2.24/2.50	       | X0 != X1
2.24/2.50	       | ~ sk_E(X1, X2)
2.24/2.50	       | X0(sk_Y(X1))
2.24/2.50	       | sk_P != X1
2.24/2.50	       | cC != cC),
2.24/2.50	    inference('sup-', [status(thm)], ['5', '17'])).
2.24/2.50	tff('19', plain,
2.24/2.50	    ![X0 : a > $o > $o, X1 : a > $o > $o, X2 : a]:
2.24/2.50	      (sk_P != X1 | X0(sk_Y(X1)) | ~ sk_E(X1, X2) | X0 != X1),
2.24/2.50	    inference('simplify', [status(thm)], ['18'])).
2.24/2.50	tff('20', plain,
2.24/2.50	    ![X0 : a > $o, X1 : a > $o > $o, X2 : a > $o > $o]:
2.24/2.50	      (~ $true
2.24/2.50	       | sk_P(X0)
2.24/2.50	       | sk_E(X1) != X0
2.24/2.50	       | X2 != X1
2.24/2.50	       | X2(sk_Y(X1))
2.24/2.50	       | sk_P != X1),
2.24/2.50	    inference('sup-', [status(thm)], ['1', '19'])).
2.24/2.50	tff('21', plain,
2.24/2.50	    ![X0 : a > $o, X1 : a > $o > $o, X2 : a > $o > $o]:
2.24/2.50	      (sk_P != X1 | X2(sk_Y(X1)) | X2 != X1 | sk_E(X1) != X0 | sk_P(X0)),
2.24/2.50	    inference('simplify', [status(thm)], ['20'])).
2.24/2.50	tff('22', plain,
2.24/2.50	    ![X0 : a > $o > $o, X1 : a > $o > $o]:
2.24/2.50	      (sk_P(sk_E(X0)) | X1 != X0 | X1(sk_Y(X0)) | sk_P != X0),
2.24/2.50	    inference('eq_res', [status(thm)], ['21'])).
2.24/2.50	tff('23', plain,
2.24/2.50	    ![X1 : a > $o > $o]: (X1(cC) | ~ X1(sk_E(X1)) | X1(sk_Y(X1))),
2.24/2.50	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.24/2.50	tff('24', plain,
2.24/2.50	    ![X1 : a > $o > $o, X2 : a > $o > $o, X3 : a > $o > $o, X4 : a > $o > $o]:
2.24/2.50	      (X4 != X1
2.24/2.50	       | X3 != X1
2.24/2.50	       | X2 != X1
2.24/2.50	       | X1(cC)
2.24/2.50	       | ~ X2(sk_E(X3))
2.24/2.50	       | X4(sk_Y(X3))),
2.24/2.50	    inference('ho.purify_applied_variable', [status(thm)], ['23'])).
2.24/2.50	tff('25', plain,
2.24/2.50	    ![X0 : a > $o > $o, X1 : a > $o > $o, X2 : a > $o > $o]:
2.24/2.50	      (X0(sk_Y(X1)) | ~ X2(sk_E(X1)) | X1(cC) | X2 != X1 | X0 != X1),
2.24/2.50	    inference('eq_res', [status(thm)], ['24'])).
2.24/2.50	tff('26', plain,
2.24/2.50	    ![X0 : a > $o > $o, X1 : a > $o > $o, X2 : a > $o > $o, X3 : a > $o > $o]:
2.24/2.50	      (X3 != X1
2.24/2.50	       | X0(sk_Y(X1))
2.24/2.50	       | ~ X2(sk_E(X1))
2.24/2.50	       | X3(cC)
2.24/2.50	       | X2 != X1
2.24/2.50	       | X0 != X1),
2.24/2.50	    inference('ho.purify_applied_variable', [status(thm)], ['25'])).
2.24/2.50	tff('27', plain,
2.24/2.50	    ![X0 : a > $o > $o, X1 : a > $o > $o, X2 : a > $o > $o]:
2.24/2.50	      (~ $true
2.24/2.50	       | X0 != X1
2.24/2.50	       | X2 != X1
2.24/2.50	       | ~ X2(sk_E(X1))
2.24/2.50	       | X0(sk_Y(X1))
2.24/2.50	       | sk_P != X1
2.24/2.50	       | cC != cC),
2.24/2.50	    inference('sup-', [status(thm)], ['26', '17'])).
2.24/2.50	tff('28', plain,
2.24/2.50	    ![X0 : a > $o > $o, X1 : a > $o > $o, X2 : a > $o > $o]:
2.24/2.50	      (sk_P != X1 | X0(sk_Y(X1)) | ~ X2(sk_E(X1)) | X2 != X1 | X0 != X1),
2.24/2.50	    inference('simplify', [status(thm)], ['27'])).
2.24/2.50	tff('29', plain,
2.24/2.50	    ![X0 : a > $o > $o, X1 : a > $o > $o, X2 : a > $o > $o]:
2.24/2.50	      (~ $true
2.24/2.50	       | sk_P != X0
2.24/2.50	       | X2(sk_Y(X0))
2.24/2.50	       | X2 != X0
2.24/2.50	       | X1 != X0
2.24/2.50	       | sk_P != X0
2.24/2.50	       | X1(sk_Y(X0))
2.24/2.50	       | sk_P != X0),
2.24/2.50	    inference('sup-', [status(thm)], ['22', '28'])).
2.24/2.50	tff('30', plain,
2.24/2.50	    ![X0 : a > $o > $o, X1 : a > $o > $o, X2 : a > $o > $o]:
2.24/2.50	      (X1(sk_Y(X0)) | X1 != X0 | X2 != X0 | X2(sk_Y(X0)) | sk_P != X0),
2.24/2.50	    inference('simplify', [status(thm)], ['29'])).
2.24/2.50	tff('31', plain,
2.24/2.50	    ![X0 : a > $o > $o, X1 : a > $o > $o]:
2.24/2.50	      (~ $true | sk_P != X1 | X0(sk_Y(X1)) | X0 != X1 | X0 != X1),
2.24/2.50	    inference('eq_fact', [status(thm)], ['30'])).
2.24/2.50	tff('32', plain,
2.24/2.50	    ![X0 : a > $o > $o, X1 : a > $o > $o]:
2.24/2.50	      (X0 != X1 | X0(sk_Y(X1)) | sk_P != X1),
2.24/2.50	    inference('simplify', [status(thm)], ['31'])).
2.24/2.50	tff('33', plain,
2.24/2.50	    ![X1 : a > $o > $o, X2 : a, X3 : a]:
2.24/2.50	      (X1(cC)
2.24/2.50	       | ~ sk_E(X1, X2)
2.24/2.50	       | sk_Y(X1, X3)
2.24/2.50	       | X3 = sk_Xx(X1)
2.24/2.50	       | ~ sk_Z(X1, X3)),
2.24/2.50	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.24/2.50	tff('34', plain,
2.24/2.50	    ![X1 : a > $o > $o, X2 : a, X3 : a, X4 : a > $o > $o]:
2.24/2.50	      (X4 != X1
2.24/2.50	       | X1(cC)
2.24/2.50	       | ~ sk_E(X4, X2)
2.24/2.50	       | sk_Y(X4, X3)
2.24/2.50	       | X3 = sk_Xx(X4)
2.24/2.50	       | ~ sk_Z(X4, X3)),
2.24/2.50	    inference('ho.purify_applied_variable', [status(thm)], ['33'])).
2.24/2.50	tff('35', plain,
2.24/2.50	    ![X0 : a, X1 : a > $o > $o, X2 : a]:
2.24/2.50	      (~ $true
2.24/2.50	       | ~ sk_Z(X1, X0)
2.24/2.50	       | X0 = sk_Xx(X1)
2.24/2.50	       | sk_Y(X1, X0)
2.24/2.50	       | ~ sk_E(X1, X2)
2.24/2.50	       | X1 != sk_P
2.24/2.50	       | cC != cC),
2.24/2.50	    inference('sup-', [status(thm)], ['34', '17'])).
2.24/2.50	tff('36', plain,
2.24/2.50	    ![X0 : a, X1 : a > $o > $o, X2 : a]:
2.24/2.50	      (X1 != sk_P
2.24/2.50	       | ~ sk_E(X1, X2)
2.24/2.50	       | sk_Y(X1, X0)
2.24/2.50	       | X0 = sk_Xx(X1)
2.24/2.50	       | ~ sk_Z(X1, X0)),
2.24/2.50	    inference('simplify', [status(thm)], ['35'])).
2.24/2.50	tff('37', plain,
2.24/2.50	    ![X0 : a > $o, X1 : a, X2 : a > $o, X3 : a > $o > $o, X4 : a]:
2.24/2.50	      (~ $true
2.24/2.50	       | sk_P(X2)
2.24/2.50	       | ~ sk_P(X0)
2.24/2.50	       | X2 != sk_Z(X3)
2.24/2.50	       | sk_Xx_28(X2, X1, X0) = sk_Xx(X3)
2.24/2.50	       | sk_Y(X3, sk_Xx_28(X2, X1, X0))
2.24/2.50	       | ~ sk_E(X3, X4)
2.24/2.50	       | X3 != sk_P),
2.24/2.50	    inference('sup-', [status(thm)], ['7', '36'])).
2.24/2.50	tff('38', plain,
2.24/2.50	    ![X0 : a > $o, X1 : a, X2 : a > $o, X3 : a > $o > $o, X4 : a]:
2.24/2.50	      (X3 != sk_P
2.24/2.50	       | ~ sk_E(X3, X4)
2.24/2.50	       | sk_Y(X3, sk_Xx_28(X2, X1, X0))
2.24/2.50	       | sk_Xx_28(X2, X1, X0) = sk_Xx(X3)
2.24/2.50	       | X2 != sk_Z(X3)
2.24/2.50	       | ~ sk_P(X0)
2.24/2.50	       | sk_P(X2)),
2.24/2.50	    inference('simplify', [status(thm)], ['37'])).
2.24/2.50	tff('39', plain,
2.24/2.50	    ![X0 : a > $o > $o, X1 : a > $o, X2 : a, X3 : a > $o, X4 : a]:
2.24/2.50	      (~ $true
2.24/2.50	       | sk_P(X3)
2.24/2.50	       | ~ sk_P(X1)
2.24/2.50	       | X3 != sk_Z(X0)
2.24/2.50	       | sk_Xx_28(X3, X2, X1) = sk_Xx(X0)
2.24/2.50	       | ~ sk_E(X0, X4)
2.24/2.50	       | X0 != sk_P
2.24/2.50	       | sk_P(X3)
2.24/2.50	       | ~ sk_P(X1)
2.24/2.50	       | sk_Y(X0) != X1),
2.24/2.50	    inference('sup-', [status(thm)], ['38', '12'])).
2.24/2.50	tff('40', plain,
2.24/2.50	    ![X0 : a > $o > $o, X1 : a > $o, X2 : a, X3 : a > $o, X4 : a]:
2.24/2.50	      (sk_Y(X0) != X1
2.24/2.50	       | X0 != sk_P
2.24/2.50	       | ~ sk_E(X0, X4)
2.24/2.50	       | sk_Xx_28(X3, X2, X1) = sk_Xx(X0)
2.24/2.50	       | X3 != sk_Z(X0)
2.24/2.50	       | ~ sk_P(X1)
2.24/2.50	       | sk_P(X3)),
2.24/2.50	    inference('simplify', [status(thm)], ['39'])).
2.24/2.50	tff('41', plain,
2.24/2.50	    ![X5 : a > $o, X6 : a > $o, X7 : a]:
2.24/2.50	      (~ sk_P(X5) | sk_Xx_28(X6, X7, X5) != X7 | sk_P(X6)),
2.24/2.50	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.24/2.50	tff('42', plain,
2.24/2.50	    ![X0 : a > $o > $o, X1 : a, X2 : a > $o, X3 : a > $o, X4 : a]:
2.24/2.50	      (sk_Xx(X0) != X1
2.24/2.50	       | sk_P(X3)
2.24/2.50	       | ~ sk_P(X2)
2.24/2.50	       | X3 != sk_Z(X0)
2.24/2.50	       | ~ sk_E(X0, X4)
2.24/2.50	       | X0 != sk_P
2.24/2.50	       | sk_Y(X0) != X2
2.24/2.50	       | sk_P(X3)
2.24/2.50	       | ~ sk_P(X2)),
2.24/2.50	    inference('sup-', [status(thm)], ['40', '41'])).
2.24/2.50	tff('43', plain,
2.24/2.50	    ![X0 : a > $o > $o, X2 : a > $o, X3 : a > $o, X4 : a]:
2.24/2.50	      (sk_Y(X0) != X2
2.24/2.50	       | X0 != sk_P
2.24/2.50	       | ~ sk_E(X0, X4)
2.24/2.50	       | X3 != sk_Z(X0)
2.24/2.50	       | ~ sk_P(X2)
2.24/2.50	       | sk_P(X3)),
2.24/2.50	    inference('simplify', [status(thm)], ['42'])).
2.24/2.50	tff('44', plain,
2.24/2.50	    ![X0 : a > $o, X1 : a > $o > $o, X2 : a]:
2.24/2.50	      (sk_P(X0)
2.24/2.50	       | ~ sk_P(sk_Y(X1))
2.24/2.50	       | X0 != sk_Z(X1)
2.24/2.50	       | ~ sk_E(X1, X2)
2.24/2.50	       | X1 != sk_P),
2.24/2.50	    inference('eq_res', [status(thm)], ['43'])).
2.24/2.50	tff('45', plain,
2.24/2.50	    ![X0 : a > $o > $o, X1 : a, X2 : a > $o]:
2.24/2.50	      (~ $true
2.24/2.50	       | sk_P != X0
2.24/2.50	       | sk_P != X0
2.24/2.50	       | X0 != sk_P
2.24/2.50	       | ~ sk_E(X0, X1)
2.24/2.50	       | X2 != sk_Z(X0)
2.24/2.50	       | sk_P(X2)),
2.24/2.50	    inference('sup-', [status(thm)], ['32', '44'])).
2.24/2.50	tff('46', plain,
2.24/2.50	    ![X0 : a > $o > $o, X1 : a, X2 : a > $o]:
2.24/2.50	      (sk_P(X2) | X2 != sk_Z(X0) | ~ sk_E(X0, X1) | sk_P != X0),
2.24/2.50	    inference('simplify', [status(thm)], ['45'])).
2.24/2.50	tff('47', plain,
2.24/2.50	    ![X0 : a > $o > $o, X1 : a]:
2.24/2.50	      (sk_P != X0 | ~ sk_E(X0, X1) | sk_P(sk_Z(X0))),
2.24/2.50	    inference('eq_res', [status(thm)], ['46'])).
2.24/2.50	tff('48', plain,
2.24/2.50	    ![X1 : a > $o > $o, X2 : a]: (X1(cC) | ~ sk_E(X1, X2) | ~ X1(sk_Z(X1))),
2.24/2.50	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.24/2.50	tff('49', plain,
2.24/2.50	    ![X1 : a > $o > $o, X2 : a, X3 : a > $o > $o, X4 : a > $o > $o]:
2.24/2.50	      (X4 != X1 | X3 != X1 | X1(cC) | ~ sk_E(X3, X2) | ~ X4(sk_Z(X3))),
2.24/2.50	    inference('ho.purify_applied_variable', [status(thm)], ['48'])).
2.24/2.50	tff('50', plain,
2.24/2.50	    ![X0 : a > $o, X1 : a > $o > $o, X2 : a > $o > $o, X3 : a > $o > $o]:
2.24/2.50	      (~ $true
2.24/2.50	       | sk_P(X0)
2.24/2.50	       | sk_E(X1) != X0
2.24/2.50	       | ~ X2(sk_Z(X1))
2.24/2.50	       | X3(cC)
2.24/2.50	       | X1 != X3
2.24/2.50	       | X2 != X3),
2.24/2.50	    inference('sup-', [status(thm)], ['1', '49'])).
2.24/2.50	tff('51', plain,
2.24/2.50	    ![X0 : a > $o, X1 : a > $o > $o, X2 : a > $o > $o, X3 : a > $o > $o]:
2.24/2.50	      (X2 != X3
2.24/2.50	       | X1 != X3
2.24/2.50	       | X3(cC)
2.24/2.50	       | ~ X2(sk_Z(X1))
2.24/2.50	       | sk_E(X1) != X0
2.24/2.50	       | sk_P(X0)),
2.24/2.50	    inference('simplify', [status(thm)], ['50'])).
2.24/2.50	tff('52', plain,
2.24/2.50	    ![X0 : a > $o > $o, X1 : a > $o > $o, X2 : a > $o > $o]:
2.24/2.50	      (sk_P(sk_E(X0)) | ~ X1(sk_Z(X0)) | X2(cC) | X0 != X2 | X1 != X2),
2.24/2.50	    inference('eq_res', [status(thm)], ['51'])).
2.24/2.50	tff('53', plain,
2.24/2.50	    ![X1 : a > $o > $o]: (X1(cC) | ~ X1(sk_E(X1)) | ~ X1(sk_Z(X1))),
2.24/2.50	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.24/2.50	tff('54', plain,
2.24/2.50	    ![X1 : a > $o > $o, X2 : a > $o > $o, X3 : a > $o > $o, X4 : a > $o > $o]:
2.24/2.50	      (X4 != X1
2.24/2.50	       | X3 != X1
2.24/2.50	       | X2 != X1
2.24/2.50	       | X1(cC)
2.24/2.50	       | ~ X2(sk_E(X3))
2.24/2.50	       | ~ X4(sk_Z(X3))),
2.24/2.50	    inference('ho.purify_applied_variable', [status(thm)], ['53'])).
2.24/2.50	tff('55', plain,
2.24/2.50	    ![X0 : a > $o > $o, X1 : a > $o > $o, X2 : a > $o > $o]:
2.24/2.50	      (~ X0(sk_Z(X1)) | ~ X2(sk_E(X1)) | X1(cC) | X2 != X1 | X0 != X1),
2.24/2.50	    inference('eq_res', [status(thm)], ['54'])).
2.24/2.50	tff('56', plain,
2.24/2.50	    ![X0 : a > $o > $o, X1 : a > $o > $o, X2 : a > $o > $o, X3 : a > $o > $o]:
2.24/2.50	      (X3 != X1
2.24/2.50	       | ~ X0(sk_Z(X1))
2.24/2.50	       | ~ X2(sk_E(X1))
2.24/2.50	       | X3(cC)
2.24/2.50	       | X2 != X1
2.24/2.50	       | X0 != X1),
2.24/2.50	    inference('ho.purify_applied_variable', [status(thm)], ['55'])).
2.24/2.50	tff('57', plain,
2.24/2.50	    ![X0 : a > $o > $o, X1 : a > $o > $o, X2 : a > $o > $o]:
2.24/2.50	      (~ $true
2.24/2.50	       | X0 != X1
2.24/2.50	       | X2 != X1
2.24/2.50	       | ~ X2(sk_E(X1))
2.24/2.50	       | ~ X0(sk_Z(X1))
2.24/2.50	       | sk_P != X1
2.24/2.50	       | cC != cC),
2.24/2.50	    inference('sup-', [status(thm)], ['56', '17'])).
2.24/2.50	tff('58', plain,
2.24/2.50	    ![X0 : a > $o > $o, X1 : a > $o > $o, X2 : a > $o > $o]:
2.24/2.50	      (sk_P != X1 | ~ X0(sk_Z(X1)) | ~ X2(sk_E(X1)) | X2 != X1 | X0 != X1),
2.24/2.50	    inference('simplify', [status(thm)], ['57'])).
2.24/2.50	tff('59', plain,
2.24/2.50	    ![X0 : a > $o > $o, X1 : a > $o > $o, X2 : a > $o > $o, X3 : a > $o > $o]:
2.24/2.50	      (~ $true
2.24/2.50	       | X2 != X3
2.24/2.50	       | X0 != X3
2.24/2.50	       | X3(cC)
2.24/2.50	       | ~ X2(sk_Z(X0))
2.24/2.50	       | X1 != X0
2.24/2.50	       | sk_P != X0
2.24/2.50	       | ~ X1(sk_Z(X0))
2.24/2.50	       | sk_P != X0),
2.24/2.50	    inference('sup-', [status(thm)], ['52', '58'])).
2.24/2.50	tff('60', plain,
2.24/2.50	    ![X0 : a > $o > $o, X1 : a > $o > $o, X2 : a > $o > $o, X3 : a > $o > $o]:
2.24/2.50	      (~ X1(sk_Z(X0))
2.24/2.50	       | sk_P != X0
2.24/2.50	       | X1 != X0
2.24/2.50	       | ~ X2(sk_Z(X0))
2.24/2.50	       | X3(cC)
2.24/2.50	       | X0 != X3
2.24/2.50	       | X2 != X3),
2.24/2.50	    inference('simplify', [status(thm)], ['59'])).
2.24/2.50	tff('61', plain,
2.24/2.50	    ![X0 : a > $o > $o, X1 : a > $o > $o, X2 : a > $o > $o]:
2.24/2.50	      (X0 != X1
2.24/2.50	       | X1(cC)
2.24/2.50	       | ~ X0(sk_Z(X1))
2.24/2.50	       | X2 != X1
2.24/2.50	       | sk_P != X1
2.24/2.50	       | ~ X2(sk_Z(X1))),
2.24/2.50	    inference('eq_res', [status(thm)], ['60'])).
2.24/2.50	tff('62', plain,
2.24/2.50	    ![X0 : a > $o > $o, X1 : a > $o > $o, X2 : a > $o > $o, X3 : a > $o > $o]:
2.24/2.50	      (X3 != X1
2.24/2.50	       | X0 != X1
2.24/2.50	       | X1(cC)
2.24/2.50	       | ~ X0(sk_Z(X3))
2.24/2.50	       | X2 != X1
2.24/2.50	       | sk_P != X3
2.24/2.50	       | ~ X2(sk_Z(X3))),
2.24/2.50	    inference('ho.purify_applied_variable', [status(thm)], ['61'])).
2.24/2.50	tff('63', plain,
2.24/2.50	    ![X0 : a > $o > $o, X1 : a > $o > $o, X2 : a > $o > $o]:
2.24/2.50	      (~ X0(sk_Z(X1))
2.24/2.50	       | sk_P != X1
2.24/2.50	       | X0 != X2
2.24/2.50	       | ~ X2(sk_Z(X1))
2.24/2.50	       | X2(cC)
2.24/2.50	       | X1 != X2),
2.24/2.50	    inference('eq_res', [status(thm)], ['62'])).
2.24/2.50	tff('64', plain,
2.24/2.50	    ![X0 : a > $o > $o, X1 : a > $o > $o, X2 : a > $o > $o, X3 : a > $o > $o]:
2.24/2.50	      (X3 != X2
2.24/2.50	       | ~ X0(sk_Z(X1))
2.24/2.50	       | sk_P != X1
2.24/2.50	       | X0 != X2
2.24/2.50	       | ~ X2(sk_Z(X1))
2.24/2.50	       | X3(cC)
2.24/2.50	       | X1 != X2),
2.24/2.50	    inference('ho.purify_applied_variable', [status(thm)], ['63'])).
2.24/2.50	tff('65', plain,
2.24/2.50	    ![X0 : a > $o > $o, X1 : a > $o > $o, X2 : a > $o > $o]:
2.24/2.50	      (X0 != X1
2.24/2.50	       | X2(cC)
2.24/2.50	       | ~ X1(sk_Z(X0))
2.24/2.50	       | sk_P != X0
2.24/2.50	       | ~ X1(sk_Z(X0))
2.24/2.50	       | X2 != X1),
2.24/2.50	    inference('eq_res', [status(thm)], ['64'])).
2.24/2.50	tff('66', plain,
2.24/2.50	    ![X0 : a > $o > $o, X1 : a > $o > $o, X2 : a > $o > $o]:
2.24/2.50	      (X2 != X1 | sk_P != X0 | ~ X1(sk_Z(X0)) | X2(cC) | X0 != X1),
2.24/2.50	    inference('simplify', [status(thm)], ['65'])).
2.24/2.50	tff('67', plain,
2.24/2.50	    ![X0 : a > $o > $o, X1 : a > $o > $o]:
2.24/2.50	      (~ $true
2.24/2.50	       | X0 != X1
2.24/2.50	       | ~ X1(sk_Z(X0))
2.24/2.50	       | sk_P != X0
2.24/2.50	       | sk_P != X1
2.24/2.50	       | cC != cC),
2.24/2.50	    inference('sup-', [status(thm)], ['66', '17'])).
2.24/2.50	tff('68', plain,
2.24/2.50	    ![X0 : a > $o > $o, X1 : a > $o > $o]:
2.24/2.50	      (sk_P != X1 | sk_P != X0 | ~ X1(sk_Z(X0)) | X0 != X1),
2.24/2.50	    inference('simplify', [status(thm)], ['67'])).
2.24/2.50	tff('69', plain,
2.24/2.50	    ![X0 : a > $o > $o, X1 : a > $o > $o, X2 : a > $o > $o]:
2.24/2.50	      (X2 != X1 | sk_P != X1 | sk_P != X0 | ~ X2(sk_Z(X0)) | X0 != X1),
2.24/2.50	    inference('ho.purify_applied_variable', [status(thm)], ['68'])).
2.24/2.50	tff('70', plain,
2.24/2.50	    ![X0 : a > $o > $o, X1 : a > $o > $o]:
2.24/2.50	      (~ X0(sk_Z(X1)) | sk_P != X1 | sk_P != X1 | X0 != X1),
2.24/2.50	    inference('eq_res', [status(thm)], ['69'])).
2.24/2.50	tff('71', plain,
2.24/2.50	    ![X0 : a > $o > $o, X1 : a > $o > $o]:
2.24/2.50	      (X0 != X1 | sk_P != X1 | ~ X0(sk_Z(X1))),
2.24/2.50	    inference('simplify', [status(thm)], ['70'])).
2.24/2.50	tff('72', plain,
2.24/2.50	    ![X0 : a > $o > $o, X1 : a]:
2.24/2.50	      (~ $true | ~ sk_E(X0, X1) | sk_P != X0 | sk_P != X0 | sk_P != X0),
2.24/2.50	    inference('sup-', [status(thm)], ['47', '71'])).
2.24/2.50	tff('73', plain, ![X0 : a > $o > $o, X1 : a]: (sk_P != X0 | ~ sk_E(X0, X1)),
2.24/2.50	    inference('simplify', [status(thm)], ['72'])).
2.24/2.50	tff('74', plain,
2.24/2.50	    ![X0 : a > $o, X1 : a > $o > $o]:
2.24/2.50	      (~ $true | sk_P(X0) | sk_E(X1) != X0 | sk_P != X1),
2.24/2.50	    inference('sup-', [status(thm)], ['1', '73'])).
2.24/2.50	tff('75', plain,
2.24/2.50	    ![X0 : a > $o, X1 : a > $o > $o]:
2.24/2.50	      (sk_P != X1 | sk_E(X1) != X0 | sk_P(X0)),
2.24/2.50	    inference('simplify', [status(thm)], ['74'])).
2.24/2.50	tff('76', plain, ![X0 : a > $o > $o]: (sk_P(sk_E(X0)) | sk_P != X0),
2.24/2.50	    inference('eq_res', [status(thm)], ['75'])).
2.24/2.50	tff('77', plain,
2.24/2.50	    ![X1 : a > $o > $o, X3 : a]:
2.24/2.50	      (X1(cC)
2.24/2.50	       | ~ X1(sk_E(X1))
2.24/2.50	       | sk_Y(X1, X3)
2.24/2.50	       | X3 = sk_Xx(X1)
2.24/2.50	       | ~ sk_Z(X1, X3)),
2.24/2.50	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.24/2.50	tff('78', plain,
2.24/2.50	    ![X1 : a > $o > $o, X3 : a, X4 : a > $o > $o, X5 : a > $o > $o]:
2.24/2.50	      (X5 != X1
2.24/2.50	       | X4 != X1
2.24/2.50	       | X1(cC)
2.24/2.50	       | ~ X4(sk_E(X5))
2.24/2.50	       | sk_Y(X5, X3)
2.24/2.50	       | X3 = sk_Xx(X5)
2.24/2.50	       | ~ sk_Z(X5, X3)),
2.24/2.50	    inference('ho.purify_applied_variable', [status(thm)], ['77'])).
2.24/2.50	tff('79', plain,
2.24/2.50	    ![X0 : a, X1 : a > $o > $o, X2 : a > $o > $o]:
2.24/2.50	      (~ sk_Z(X1, X0)
2.24/2.50	       | X0 = sk_Xx(X1)
2.24/2.50	       | sk_Y(X1, X0)
2.24/2.50	       | ~ X2(sk_E(X1))
2.24/2.50	       | X1(cC)
2.24/2.50	       | X2 != X1),
2.24/2.50	    inference('eq_res', [status(thm)], ['78'])).
2.24/2.50	tff('80', plain,
2.24/2.50	    ![X0 : a, X1 : a > $o > $o, X2 : a > $o > $o, X3 : a > $o > $o]:
2.24/2.50	      (X3 != X1
2.24/2.50	       | ~ sk_Z(X1, X0)
2.24/2.50	       | X0 = sk_Xx(X1)
2.24/2.50	       | sk_Y(X1, X0)
2.24/2.50	       | ~ X2(sk_E(X1))
2.24/2.50	       | X3(cC)
2.24/2.50	       | X2 != X1),
2.24/2.50	    inference('ho.purify_applied_variable', [status(thm)], ['79'])).
2.24/2.50	tff('81', plain,
2.24/2.50	    ![X0 : a > $o > $o, X1 : a > $o > $o, X2 : a]:
2.24/2.50	      (~ $true
2.24/2.50	       | X0 != X1
2.24/2.50	       | ~ X0(sk_E(X1))
2.24/2.50	       | sk_Y(X1, X2)
2.24/2.50	       | X2 = sk_Xx(X1)
2.24/2.50	       | ~ sk_Z(X1, X2)
2.24/2.50	       | sk_P != X1
2.24/2.50	       | cC != cC),
2.24/2.50	    inference('sup-', [status(thm)], ['80', '17'])).
2.24/2.50	tff('82', plain,
2.24/2.50	    ![X0 : a > $o > $o, X1 : a > $o > $o, X2 : a]:
2.24/2.50	      (sk_P != X1
2.24/2.50	       | ~ sk_Z(X1, X2)
2.24/2.50	       | X2 = sk_Xx(X1)
2.24/2.50	       | sk_Y(X1, X2)
2.24/2.50	       | ~ X0(sk_E(X1))
2.24/2.50	       | X0 != X1),
2.24/2.50	    inference('simplify', [status(thm)], ['81'])).
2.24/2.50	tff('83', plain,
2.24/2.50	    ![X0 : a > $o > $o, X1 : a]:
2.24/2.50	      (~ $true
2.24/2.50	       | sk_P != X0
2.24/2.50	       | sk_P != X0
2.24/2.50	       | sk_Y(X0, X1)
2.24/2.50	       | X1 = sk_Xx(X0)
2.24/2.50	       | ~ sk_Z(X0, X1)
2.24/2.50	       | sk_P != X0),
2.24/2.50	    inference('sup-', [status(thm)], ['76', '82'])).
2.24/2.50	tff('84', plain,
2.24/2.50	    ![X0 : a > $o > $o, X1 : a]:
2.24/2.50	      (~ sk_Z(X0, X1) | X1 = sk_Xx(X0) | sk_Y(X0, X1) | sk_P != X0),
2.24/2.50	    inference('simplify', [status(thm)], ['83'])).
2.24/2.50	tff('85', plain,
2.24/2.50	    ![X0 : a > $o, X1 : a, X2 : a > $o, X3 : a > $o > $o]:
2.24/2.50	      (~ $true
2.24/2.50	       | sk_P(X2)
2.24/2.50	       | ~ sk_P(X0)
2.24/2.50	       | X2 != sk_Z(X3)
2.24/2.50	       | sk_P != X3
2.24/2.50	       | sk_Y(X3, sk_Xx_28(X2, X1, X0))
2.24/2.50	       | sk_Xx_28(X2, X1, X0) = sk_Xx(X3)),
2.24/2.50	    inference('sup-', [status(thm)], ['7', '84'])).
2.24/2.50	tff('86', plain,
2.24/2.50	    ![X0 : a > $o, X1 : a, X2 : a > $o, X3 : a > $o > $o]:
2.24/2.50	      (sk_Xx_28(X2, X1, X0) = sk_Xx(X3)
2.24/2.50	       | sk_Y(X3, sk_Xx_28(X2, X1, X0))
2.24/2.50	       | sk_P != X3
2.24/2.50	       | X2 != sk_Z(X3)
2.24/2.50	       | ~ sk_P(X0)
2.24/2.50	       | sk_P(X2)),
2.24/2.50	    inference('simplify', [status(thm)], ['85'])).
2.24/2.50	tff('87', plain,
2.24/2.50	    ![X0 : a > $o > $o, X1 : a > $o, X2 : a, X3 : a > $o]:
2.24/2.50	      (~ $true
2.24/2.50	       | sk_P(X3)
2.24/2.50	       | ~ sk_P(X1)
2.24/2.50	       | X3 != sk_Z(X0)
2.24/2.50	       | sk_P != X0
2.24/2.50	       | sk_Xx_28(X3, X2, X1) = sk_Xx(X0)
2.24/2.50	       | sk_P(X3)
2.24/2.50	       | ~ sk_P(X1)
2.24/2.50	       | sk_Y(X0) != X1),
2.24/2.50	    inference('sup-', [status(thm)], ['86', '12'])).
2.24/2.50	tff('88', plain,
2.24/2.50	    ![X0 : a > $o > $o, X1 : a > $o, X2 : a, X3 : a > $o]:
2.24/2.50	      (sk_Y(X0) != X1
2.24/2.50	       | sk_Xx_28(X3, X2, X1) = sk_Xx(X0)
2.24/2.50	       | sk_P != X0
2.24/2.50	       | X3 != sk_Z(X0)
2.24/2.50	       | ~ sk_P(X1)
2.24/2.50	       | sk_P(X3)),
2.24/2.50	    inference('simplify', [status(thm)], ['87'])).
2.24/2.50	tff('89', plain,
2.24/2.50	    ![X0 : a > $o > $o, X1 : a, X2 : a > $o, X3 : a > $o]:
2.24/2.50	      (sk_Xx(X0) != X1
2.24/2.50	       | sk_P(X3)
2.24/2.50	       | ~ sk_P(X2)
2.24/2.50	       | X3 != sk_Z(X0)
2.24/2.50	       | sk_P != X0
2.24/2.50	       | sk_Y(X0) != X2
2.24/2.50	       | sk_P(X3)
2.24/2.50	       | ~ sk_P(X2)),
2.24/2.50	    inference('sup-', [status(thm)], ['88', '41'])).
2.24/2.50	tff('90', plain,
2.24/2.50	    ![X0 : a > $o > $o, X2 : a > $o, X3 : a > $o]:
2.24/2.50	      (sk_Y(X0) != X2 | sk_P != X0 | X3 != sk_Z(X0) | ~ sk_P(X2) | sk_P(X3)),
2.24/2.50	    inference('simplify', [status(thm)], ['89'])).
2.24/2.50	tff('91', plain,
2.24/2.50	    ![X0 : a > $o, X1 : a > $o > $o]:
2.24/2.50	      (sk_P(X0) | ~ sk_P(sk_Y(X1)) | X0 != sk_Z(X1) | sk_P != X1),
2.24/2.50	    inference('eq_res', [status(thm)], ['90'])).
2.24/2.50	tff('92', plain,
2.24/2.50	    ![X0 : a > $o > $o, X1 : a > $o]:
2.24/2.50	      (~ $true
2.24/2.50	       | sk_P != X0
2.24/2.50	       | sk_P != X0
2.24/2.50	       | sk_P != X0
2.24/2.50	       | X1 != sk_Z(X0)
2.24/2.50	       | sk_P(X1)),
2.24/2.50	    inference('sup-', [status(thm)], ['32', '91'])).
2.24/2.50	tff('93', plain,
2.24/2.50	    ![X0 : a > $o > $o, X1 : a > $o]:
2.24/2.50	      (sk_P(X1) | X1 != sk_Z(X0) | sk_P != X0),
2.24/2.50	    inference('simplify', [status(thm)], ['92'])).
2.24/2.50	tff('94', plain, ![X0 : a > $o > $o]: (sk_P != X0 | sk_P(sk_Z(X0))),
2.24/2.50	    inference('eq_res', [status(thm)], ['93'])).
2.24/2.50	tff('95', plain,
2.24/2.50	    ![X0 : a > $o > $o]: (~ $true | sk_P != X0 | sk_P != X0 | sk_P != X0),
2.24/2.50	    inference('sup-', [status(thm)], ['94', '71'])).
2.24/2.50	tff('96', plain, ![X0 : a > $o > $o]: sk_P != X0,
2.24/2.50	    inference('simplify', [status(thm)], ['95'])).
2.24/2.50	tff('97', plain, $false, inference('eq_res', [status(thm)], ['96'])).
2.24/2.50	
2.24/2.50	% SZS output end Refutation
2.24/2.50	EOF
